1. Solid Mechanics
Course No. ME213

2. Thick walled pressure vessels
Considerations σl σr r z ro ri σr σt pi po
Applications
pi = 0
Submarine
Vacuum chamber
Shrink fit
Buried pipe
po = 0
Gun barrel
Liquid- or gas-carrying pipe
Hydraulic cylinder
Gas storage tank
ME213 Solid Mechanics

3. Thick walled pressure vessels
Applications
pi = 0
Submarine
Vacuum chamber
Shrink fit
Buried pipe
po = 0
Gun barrel
Liquid- or gas-carrying pipe
Hydraulic cylinder
Gas storage tank
ME213 Solid Mechanics

4. Thick walled pressure vessels
Stresses in thick cylinder
In general the stress equations of equilibrium without body forces can be given as
...(1)
ME213 Solid Mechanics

5. Thick walled pressure vessels
Stresses in thick cylinder
In general the stress equations of equilibrium without body forces can be given as
...(2)
ME213 Solid Mechanics

6. Thick walled pressure vessels
Stresses in thick cylinder
In a plane stress situation if the cylinder ends are free to expand
and due to uniform radial deformation and symmetry
The equation of equilibrium reduces to
σz = 0
τrz = τθz = τrθ = 0
This can be written in the following form:
...(3)
ME213 Solid Mechanics

7. Thick walled pressure vessels
Stresses in thick cylinder
If we consider a general case with body forces such as centrifugal forces in the case of a rotating cylinder or disc then the equations reduce to
which may be written as
...(4)
It is convenient to solve the general equation so that a variety of problems may be solved.
ME213 Solid Mechanics

8. Thick walled pressure vessels
Strains in thick cylinder
Representation of radial and circumferential strain.
The strains εr and εθ may be given by
...(5)
...(6)
ME213 Solid Mechanics

9. Thick walled pressure vessels
Strains in thick cylinder
Combining above equations we have
...(7)
Now from equation (4) we may write
and combining this with equation (7) we may arrive at
...(8)
For a non-rotating thick cylinder with internal and external pressures pi and po we substitute ω = 0 in equation (8) and this gives
...(9)
ME213 Solid Mechanics

10. Thick walled pressure vessels
Strains in thick cylinder
A standard solution for equation (9) is
σr = c rn
where c and n are constants.
Substituting this in equation (9) and also combining with equation (3) we have
...(10)
where c1 and c2 are constants
ME213 Solid Mechanics